Solve for $b$. $3-2(b-2)=2-7b$ $b =$
Solution: We need to manipulate the equation to get $ b $ by itself. $\begin{aligned} 3-2(b-2) &= 2-7b \\\\ 3-2b+4 &= 2-7b~~~~~~~~~~\gray{\text{Distribute}}\\\\ -2b+7 &= 2-7b~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ -2b+7{+7b} &= 2-7b{+7b} ~~~~~~~~~~\gray{\text{Add 7b to each side}}\\\\ 5b+7 &=2 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 5b+7{-7} &=2 {-7} ~~~~~~~~~~\gray{\text{Subtract 7 from each side}}\\\\ 5b&=-5 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{5b}{{5}}&= \dfrac{-5}{{5}}~~~~~~~~~~\gray{\text{Divide each side by 5}} \\\\ b &= {-1} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ b = { -1 }~~~~~~~~$ [Let's check our work!]